Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cstddef>
       7             : 
       8             : /// \cond
       9             : class DataVector;
      10             : class Matrix;
      11             : /// \endcond
      12             : 
      13             : namespace intrp {
      14             : /*!
      15             :  * \brief Computes the matrix for polynomial interpolation of a non-periodic
      16             :  * function known at the set of points \f$x_{source}\f$ to the set of points
      17             :  * \f$x_{target}\f$
      18             :  *
      19             :  * \details The algorithm is from \cite Fornberg1998.  The returned matrix
      20             :  * \f$M\f$ will have \f$n_{target}\f$ rows and \f$n_{source}\f$ columns so that
      21             :  * \f$f_{target} = M f_{source}\f$
      22             :  *
      23             :  * \note The accuracy of the interpolation will depend upon the number and
      24             :  * distribution of the source points.  It is strongly suggested that you
      25             :  * carefully investigate the accuracy for your use case.
      26             :  */
      27             : template <typename TargetDataType>
      28           1 : Matrix fornberg_interpolation_matrix(const TargetDataType& x_target,
      29             :                                      const DataVector& x_source);
      30             : 
      31             : /*!
      32             :  * \brief Computes the matrix for interpolating a periodic function known at the
      33             :  * set of \f$n\f$ equally spaced points on the periodic domain \f$[0, 2 \pi]\f$
      34             :  * to the set of points \f$x_{target}\f$
      35             :  *
      36             :  * \details The returned matrix \f$M\f$ will have \f$n_{target}\f$ rows and
      37             :  * \f$n_{source}\f$ columns so that \f$f_{target} = M f_{source}\f$
      38             :  * Formally, this computes the sum
      39             :  * \f[ n w_j = 1 + 2 \sum_{k=1}^{\lfloor (n-1)/2 \rfloor} \cos(k(x - X_j))
      40             :  *     \left[ + \cos\left(\frac{n}{2}(x - X_j)\right) \right] \f]
      41             :  * for each target point \f$x\f$, where \f$ X_j = \frac{2 \pi j}{n}\f$, and
      42             :  * the term in brackets is evaluated only if \f$n\f$ is even.
      43             :  *
      44             :  */
      45             : template <typename TargetDataType>
      46           1 : Matrix fourier_interpolation_matrix(const TargetDataType& x_target,
      47             :                                     size_t n_source_points);
      48             : }  // namespace intrp